The concept of number is fundamental in learning mathematics. Some students still have a weak number concept at the start of the formal school mathematics. As an example, when adding small integers, the student must first figure out the numbers to be added on the fingers and, only thereafter, add them, by starting the counting all over again. What is problematic in view of learning is that a weak number concept makes it difficult for the student to see the relationships between the numbers. However, in understanding learning of mathematics, it is important to see these relationships.
Learning the basic counting skills is also an essential part of the primary school mathematics. Most of the tasks used in the teaching are productive-type tasks resulting in neither algebra-supportive learning nor abductive reasoning. Applicative tasks and problem solving may remain out of reach for a student with weak counting skills, and it can be difficult to teach application to him/her.
Abduction is a weaker form of reasoning than induction and deduction, aiming at understanding the processes related to innovation and creativity. The humans' ability to simultaneously consider many different options is regarded as the starting point for abduction. Besides, abduction is often compared to the work of a detective where retrospective thinking is used for finding out what caused the outcome. Abductive reasoning is needed in order to be capable of the application required in problem solving and, on the other hand, in the understanding-based learning of algebra.
Because of the restricted working memory capacity, the size of the subitization range is of importance in the learning as well. Subitization refers to the fast enumeration of small quantities of items without counting. As an example, the fast enumeration of dice and domino numbers is based on subitization.
The relationships between quantities may remain unclear for many persons to be taught, especially for young primary and secondary school students. Many of them may see the counting operations 3+2 and 2+3 as totally different counting operations. Many students of the last primary and secondary school grades may still add or subtract by actually folding their fingers up or down.
The basic counting operations being fundamental in any learning of mathematics, it is apparent that missing these basic skills, not understanding the relationships between numbers, presents huge difficulties for the students later on. Difficulties in a subject of instruction may have more long-term consequences affecting the student's self-esteem and thus also his/her risk of exclusion.